| 摘要 |
Patterns (e.g, such as images, waveforms such as sounds, electromagnetic waves, or other signals, etc.) are synthesized, modulated and/or analyzed through the use of a computer programmed with a novel mathematical formula. The formula acts as a linear operator and can be used to create a variety of shapes, waveforms, and other representations. The formula greatly enhances ability in computer operations and provides a great savings in computer memory and a substantial increase in computing power. |
| 主权项 |
1. A method for display of widely variable naturalistic scenery, including simulated plants, simulated other organisms or simulated landscapes, on an amusement device with minimized data storage and processing requirements, the method comprising:
creating with computer hardware a first shape that corresponds to at least a portion of a simulated natural form, including at least a portion of a simulated plant, a simulated other organism or a simulated landscape, based on a first set of parameter values input by said computer hardware into a representation of a formula that establishes shape position with respect to angle as: shape position corresponds to a fraction in which the denominator of said fraction has a variable root parameter (n1) set as the root of an expression including the absolute values of two terms, with the absolute value of a first term of said two terms being to an exponent based on a variable first exponent parameter (n2) and the absolute value of a second term of said two terms being to an exponent based on a variable second exponent parameter (n3), wherein said first term includes an axis sub term, having a first axis parameter (1/a or A), that is multiplied by a cosine sub term including the cosine of a value including a first rotational symmetry parameter (m1) times an angle, and wherein said second term includes an axis sub term, having a second axis parameter (1/b or B), that is multiplied by a sine sub term including the sine of a value including a second rotational symmetry parameter (m2) times an angle;
wherein (i) said first and second axis parameters, said root parameter (n1), said first and second exponent parameters (n2, n3) and said first and second rotational symmetry parameters (m1, m2) are finite real numbers, (ii) said root parameter (n1) and said first and second axis parameters are not equal to zero, and (iii) said first and second axis parameters, said root parameter (n1), said first and second exponent parameters (n2, n3) and said first and second rotational symmetry parameters (m1, m2) are not equal to 1; displaying on a monitor of the amusement device a naturalistic image based on said first shape; creating with said computer hardware additional shapes including said computer hardware inputting modified parameter values into said representation of said formula; generating a positionwise display of a naturalistic scenery by displaying with said monitor additional naturalistic images based on said additional shapes, said additional naturalistic images being displayed on said monitor separated positionwise from said naturalistic image for said positionwise display of the naturalistic scenery; whereby allowing display of widely variable naturalistic scenery, including simulated organisms, simulated plants or simulated landscapes, with minimized data storage and processing requirements due to minimized storage requirements for said parameter values and processing with said representation of said formula. |
